/*
 * @BEGIN LICENSE
 *
 * Psi4: an open-source quantum chemistry software package
 *
 * Copyright (c) 2007-2024 The Psi4 Developers.
 *
 * The copyrights for code used from other parties are included in
 * the corresponding files.
 *
 * This file is part of Psi4.
 *
 * Psi4 is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published by
 * the Free Software Foundation, version 3.
 *
 * Psi4 is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License along
 * with Psi4; if not, write to the Free Software Foundation, Inc.,
 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * @END LICENSE
 */

#ifndef _psi_src_lib_libmints_zora_h_
#define _psi_src_lib_libmints_zora_h_

#include "psi4/libmints/typedefs.h"
#include <map>

namespace psi {

class BasisSet;
class DFTGrid;
class Options;
class BasisFunctions;

/*! \ingroup MINTS
 *  \class ZORA
 *  \brief Scalar relativistic kinetic integral through zeroth-order regular approximation (ZORA).
 *
 *  \details Here we use the model potential proposed by van Wüllen in 
 *  *Molecular density functional calculations in the regular relativistic approximation*
 *  (https://doi.org/10.1063/1.476576/). The exact values of the model potential come from
 *  NWCHEM (https://www.nwchem-sw.org/). Given atomic orbital :math:`\chi`, we evaluate the
 *  following integral on a grid:
 *
 *  :math:`T^\text{SR}_{ij}=\int d\mathbf{r}^3 \frac{c^2}{2c^2-v_\text{eff} (\mathbf{r})}
 *  \nabla\chi_i^\dagger(\mathbf{r}) \cdot\nabla\chi_j(\mathbf{r})`
 *
 *  The effective potential :math:`v_\text{eff}(\mathbf{r})` is the potential experienced
 *  at a point due to nuclear attraction and electron repulsion. The generated matrix
 *  replaces the kinetic energy for SCF etc. Because this is only evaluated once, don't
 *  cheap out on the grid! The ZORA time is usually negligible.
 *
 *  \author Nathan Gillispie, University of Memphis, 2025
 */
class PSI_API ZORA {
   public:
	ZORA(std::shared_ptr<Molecule>, std::shared_ptr<BasisSet>, Options&);
	~ZORA();

    /*! @{
     * Fills an empty SharedMatrix with the computed ZORA kinetic integral.
     * @param T Shared matrix object that will hold the ZORA kinetic integrals.
     */
    void compute(SharedMatrix);
    /*! @} */

   private:
    std::shared_ptr<Molecule> molecule_;
    std::shared_ptr<BasisSet> primary_;
	std::shared_ptr<DFTGrid> grid_;
	Options& options_;
    /*! Purpose of the map: the ``block->index()`` does not index like ``grid_->blocks()``.
     *  For multithreading to work, this is a solution.
     */
    std::shared_ptr<std::map<int, SharedVector>> veff_;


	/// Initializes grid_ with options, prints details
	void setup();
	/// Fills veff_ with effective potential for each point in a block.
	void compute_veff();
	/// Creates same structure as above but all zeros. TSR->T as veff->0
	void compute_debug_veff();
	/// Uses veff_ to compute the Scalar Relativistic Kinetic Energy Matrix
	void compute_TSR(std::vector<std::shared_ptr<BasisFunctions>>, SharedMatrix&);

    /*! I'm so sorry.
     *  These are the contraction coefficients and exponents of the model basis. The
     *  last array indexes the atoms by atomic number.
     */
	static constexpr double coeffs[2919] = {0.0063990067,0.0745660339,0.3008381442,0.4565180734,0.1616787418,
0.0016101508,0.0213576449,0.1264356558,0.4071300039,0.7131028835,0.5945686398,0.1357950212,
0.0020540716,0.0273399604,0.1614536361,0.5044307717,0.7988661637,0.4659750757,-0.0763562345,0.1347347496,0.6984222586,0.2830795469,
0.0018095592,0.0233365669,0.1344604469,0.4309865449,0.7632086400,0.5763421155,-0.1393240219,0.8973583924,1.0839816236,0.2278401323,
0.0009979693,0.0126484176,0.0801916785,0.3104634400,0.6977984882,0.7349917341,0.0863085253,-0.2723303441,0.7034437169,1.6160197688,0.8986562511,0.1308103543,
0.0010630706,0.0133139323,0.0827899962,0.3164207443,0.7055795347,0.7260001690,0.0741510606,-0.1822964940,1.0955869158,1.9328237921,1.0646209184,0.1699463601,
0.0009232791,0.0110954733,0.0694478748,0.2791256526,0.6703733222,0.7508849172,0.1189438584,-0.1443152618,1.3931726662,2.3275865458,1.3049047286,0.2178569434,
0.0005901319,0.0053239186,0.0288242994,0.1289170274,0.3997710394,0.7314832004,0.5792052835,-0.1208357248,0.9269659756,2.0190117290,2.1393639103,1.0111877476,0.1501914617,
0.0006658911,0.0054095626,0.0223598594,0.1060264486,0.3609740709,0.7211671721,0.6318974087,-0.0829411114,1.3971638449,2.5607470310,2.1860201452,0.9507535001,0.1397561769,
0.0006768561,0.0070464403,0.0367569395,0.1385891216,0.3869842934,0.6890719359,0.5770902899,-0.0755015652,1.5362076615,2.9676789175,2.5440367432,1.0528751516,0.1384872149,
0.0007252885,0.0075077428,0.0363758729,0.1219417203,0.3395938753,0.6648767422,0.6383083847,-0.0572244666,1.9365303914,3.4872987180,2.2702140398,0.4212451579,0.1088265136,0.7175769690,0.3062030503,
0.0006284320,0.0066776737,0.0326349190,0.1203719831,0.3594760994,0.6865933679,0.6137613114,-0.0866002143,2.1419332799,3.8115249408,2.0305159058,-0.1028791630,0.5258312499,1.4436183630,0.4159118515,
0.0009210356,0.0117355703,0.0763449080,0.3008679627,0.6851197240,0.7047642868,-0.0913877380,2.0000088424,3.8406547978,2.2009707867,-0.2447273574,0.6283420166,1.6726830615,1.0214623843,0.1922397186,
0.0008879891,0.0113506716,0.0743521110,0.2949575288,0.6812129888,0.7090832519,-0.1092178152,1.9529291335,3.9055653035,2.2679869040,-0.5242481374,0.3972851522,2.3710444240,1.6526017335,0.3142087606,
0.0007919386,0.0105233253,0.0721869372,0.2968653322,0.6926570097,0.7000586357,-0.1340286627,1.4023293937,3.3804592703,3.1330673878,-1.1373596133,1.7018482895,2.9030987334,1.6902111249,0.2872908977,
0.0007637109,0.0098968474,0.0676541543,0.2827777525,0.6797531939,0.7198392884,-0.1175102764,2.0367188324,3.8635905942,2.2429875270,-1.0470661107,1.4343047172,3.3019554470,2.1615132092,0.3628211127,
0.0008831372,0.0112397001,0.0760679017,0.3153700371,0.7480685580,0.8424836549,-0.3325813541,0.1083117007,3.3232015151,4.4185500624,-2.2008567862,2.6144185784,4.2068493167,2.4677163482,0.4002776298,
0.0008130640,0.0097971536,0.0641968449,0.2652230491,0.6523773144,0.7414739685,-0.1154385316,2.6356613486,4.5436194425,1.0595584696,-1.7397305116,2.7080118557,4.5228983315,2.3303011976,0.3212370032,
0.0004025842,0.0045849421,0.0287959974,0.1215282027,0.3510891838,0.6495567383,0.6006072967,-0.1506681321,2.4994433434,4.5819022642,1.4051226628,-2.1202959317,2.6890504081,4.1104756138,2.6278967300,1.5454698595,-1.1957307695,0.0734932624,0.7278914563,0.4493842877,
0.0002873755,0.0025540683,0.0149947556,0.0748737339,0.2783532100,0.6530682916,0.7164852049,-0.0654396224,-0.0879921980,2.9284472377,4.9510324430,0.8990329528,-2.8051719410,3.9189837431,5.2544340559,1.2051828278,-0.8446597620,1.1917174093,1.4692886638,0.2445275503,
0.0004175650,0.0055467572,-0.0010185217,0.0303287046,0.1322119728,0.3905135253,0.7063055290,0.5485317332,-0.2307797651,0.2442252068,3.2283991632,4.6118021055,-2.8792580874,2.2970803021,5.9948180732,2.9164479333,-0.0098430987,1.0073173195,1.6536851021,0.3532684802,
0.0003969903,0.0037172477,0.0018847141,0.0277161682,0.1243062027,0.3791463215,0.7124021785,0.5799130083,-0.2534329580,0.0610283400,3.2450104089,4.7906413336,-2.5454887531,2.9006764840,5.8838791318,2.6866141415,0.2035616538,1.2195875174,1.6427884874,0.3356513815,
0.0003120375,0.0025950741,0.0141896886,0.0678255577,0.2499560650,0.6004902714,0.7151813872,0.1091799298,-0.1859882233,3.0838671085,4.9859045339,-3.0404524289,0.9870922715,5.4675193275,5.3822541202,1.3643164903,-0.0981506778,1.6034546026,1.4462874831,0.2441653810,
0.0003628816,0.0031894809,0.0041816945,0.0224018741,0.1014612999,0.3169798025,0.6481742157,0.6432211640,-0.1399702396,-0.0308551006,3.0092151597,4.9765249311,-2.9091175729,3.0736462151,6.3571450161,3.7081379869,1.5269360059,1.3451113641,1.1201355740,0.2231182471,
0.0002622490,0.0023196093,0.0108389494,0.0429124996,0.1529063681,0.3923003315,0.6167931219,0.5149156011,-0.2087828945,2.5936884150,5.0030891336,0.5867195521,-3.0717248643,3.3215904126,7.4053693435,3.6163856438,1.2776402092,1.6049157633,0.9703341569,0.1675263987,
0.0003117181,0.0029331723,0.0159862681,0.0672695058,0.2284754724,0.5419730150,0.6685238658,0.2217763188,-0.2023848163,3.0260662110,5.0530772203,-1.3810189687,-1.7671737925,5.1590551641,7.3483909021,3.0431393598,1.2748582345,1.4530928088,1.0556480621,0.1900002784,
0.0004195763,0.0054774291,-0.0027518475,0.0230329846,0.0953648393,0.2997574957,0.6330464805,0.6724087555,-0.0930467714,-0.1917033205,2.8744286795,5.1714786306,-3.0075487466,3.2864197548,7.1348664528,4.6933592895,1.8694277711,1.7157327874,1.5179752749,0.3018544844,
0.0003294560,0.0029566039,0.0138430994,0.0519505856,0.1807108861,0.4594996110,0.6623837565,0.3849404961,-0.2185863739,2.8924225708,5.0357310143,-3.3725780375,3.0418508872,7.7967542975,5.4448701135,1.9033083352,0.8128402576,1.5340495639,1.1811037728,0.1916191041,
0.0003208400,0.0030352822,0.0170440368,0.0750144951,0.2584331695,0.6064386678,0.7275259814,0.0038710239,-0.2525637263,2.7320212509,5.2141927126,-2.8023984670,4.3335118774,7.8349491950,4.0941936561,2.1549188490,1.8284942696,1.3191595989,0.7261372350,0.1257000521,
0.0003231110,0.0031143337,0.0161297797,0.0562815372,0.1691954079,0.4250609321,0.6824564906,0.4517960555,-0.2580656328,2.8654855684,4.9697521104,-3.7281105048,3.7293606005,8.7455221167,5.8656256836,1.7319953297,1.0965252683,1.7254343548,1.2414078374,0.2107096201,
0.0002916019,0.0027492371,0.0152710006,0.0661240565,0.2258035957,0.5440929129,0.7305492935,0.2894197881,-0.3580526026,2.7587701073,5.0855992764,-3.9440345952,3.6236208898,9.2960853628,12.7260392956,-8.9398994672,4.4914781157,2.0155808101,2.5560893932,-1.8399293943,1.5162053808,0.1381459412,
0.0002609791,0.0020270791,0.0027148225,0.0174027022,0.0728515895,0.2245933228,0.4469345890,0.4300635683,0.5058514823,-0.2412862926,2.6563433637,5.2134903222,-4.1188479256,3.8094101547,9.2180407994,6.4217078060,1.8497684941,1.1114397415,1.3342667752,1.9206249574,0.9682747200,0.1540669492,
0.0002552873,0.0022766958,0.0106283921,0.0351854636,0.1146866237,0.3278587667,0.6359792015,0.6022180323,-0.1913812915,3.1220592359,4.8693771879,-2.6203685691,-0.1981506663,7.6274198323,9.2332923177,3.3904617808,-1.3952353052,2.1844952271,2.6753522153,1.0434493604,1.3089113336,0.2212288782,
0.0002260275,0.0018817394,0.0018429003,0.0154127402,0.0725276225,0.2518652001,0.5871803308,0.7009116628,0.0715302498,-0.2549217333,2.6568431325,5.2355383760,-6.6113215793,4.9442815553,8.2601810674,7.0984986948,3.0222365796,1.4693305199,2.7884233662,1.9520728077,1.4771560825,0.2583026573,
0.0001938671,0.0015643799,0.0042774898,0.0176242155,0.0801831684,0.2708616391,0.6065340942,0.6539668611,0.0606630190,-0.2111270423,2.8588973772,5.0819756579,-3.7924494238,1.3870340667,7.9184979022,7.7484371688,3.2617755863,-0.4211727084,3.6348623637,3.8848224270,1.7258962435,0.2266816472,
0.0002297756,0.0017867440,0.0034670302,0.0142063991,0.0627598126,0.1999228716,0.4474298859,0.6255112549,0.4122796049,-0.2406499503,3.0349252707,4.9357984865,-4.3582750731,1.4508604915,9.6680133272,9.3442568714,0.3109233292,-1.4566565139,4.6975828699,4.7396312107,1.8994600477,0.2065362536,
0.0002191913,0.0017674595,0.0045066879,0.0165688569,0.0747975122,0.2532937479,0.5903561718,0.7217826641,0.0441513761,-0.2857031315,2.7036075981,5.2769818933,0.3361211885,-3.5437246318,9.6561323079,9.9728751952,-0.3787535916,-1.7723423711,5.3857895994,5.2628156446,1.4357490884,0.0620683929,-0.7076426043,1.3269586913,0.5616230630,
0.0001915731,0.0010698709,0.0019917095,0.0112779909,0.0391626377,0.1057991898,0.2800473843,0.5769953954,0.6454989501,0.0580178656,-0.2570281564,2.6535742265,5.2757510288,-4.2030958223,3.7104190377,11.0950557323,6.2278242470,-3.1094593805,3.1970821707,6.1582513573,2.8326694901,-0.1100644809,0.8004042572,1.6098650408,0.3986986843,
0.0001775368,0.0013826145,0.0010704799,0.0075791770,0.0275227866,0.0932074419,0.2813025099,0.6060481773,0.6772537675,-0.0984016282,-0.5704830801,2.9134302939,5.4852539018,-4.0356936265,3.0686605629,10.0537514423,7.8722113718,-2.3577270400,3.6494623013,5.3115515943,2.5456655061,-0.1285333694,1.4607758885,1.8254222041,0.3091091855,
0.0001864328,0.0012428301,0.0012264223,0.0075174426,0.0212386900,0.0751089066,0.2429574839,0.5601256623,0.7107184010,0.1154121239,-0.3102518576,2.5558891781,5.4197944024,-4.1649054980,6.8026686305,11.3894301484,2.8291416230,-3.5091811008,5.4562956056,6.6118538645,3.1149291445,-2.0638349977,1.9792306433,1.8367128024,0.3164930157,
0.0002051557,0.0019799954,-0.0002194122,0.0092991767,0.0292335582,0.0698580168,0.1982900374,0.4589337821,0.6760455911,0.4463537126,-0.3729682195,2.9268974102,5.0406008133,-4.1548796470,7.4344299213,11.4343004658,2.5058182671,-3.4617432476,4.7011343405,6.0210041203,2.6269770204,1.1418382007,1.6560532034,1.3608400248,0.2497177126,
0.0001901630,0.0014250322,0.0007792889,0.0100402633,0.0379535714,0.1101044881,0.2825317751,0.5836600323,0.6698751622,-0.0403406334,-0.5410740685,2.5541247741,5.6868044481,-4.4954519037,5.6070102826,8.0296174782,8.2299746913,-4.0787213024,4.4680995402,7.3520906807,3.5285362134,2.0821254276,1.0302125687,0.6827280928,0.2077039334,
0.0001615946,0.0012636713,0.0049339848,0.0110285236,0.0237335715,0.0864456642,0.2664376003,0.5873446933,0.6914993652,0.0071901916,-0.2598682295,3.0146208806,5.7315690659,-1.8305817470,-7.6606715509,10.6057294466,15.3386737233,-4.0289117905,6.7590008575,6.6303657428,2.4586332438,1.4379823215,1.8203183132,1.1282832395,0.1748176228,
0.0001538895,0.0012376853,0.0043694326,0.0069283271,0.0293720495,0.0978806711,0.2745737087,0.5772510769,0.6709305903,0.0171489106,-0.3337866810,2.4895183849,5.5458123014,-5.2970015500,2.2024226939,12.1590461677,9.2983389064,-5.0076018945,4.2123388916,7.1427529770,4.9433563355,2.3326019191,1.2646719952,1.1396567291,0.2280264820,
0.0001591198,0.0012077913,0.0032625072,0.0073879354,0.0286400148,0.0964944021,0.2806726552,0.6009445761,0.6856618368,-0.0667550998,-1.5082386685,3.4905636668,5.7786277524,-4.5289165806,7.0069323735,4.7767193032,10.9972651078,-5.3040588434,6.0280136276,6.9290993839,4.6427435164,2.5627404960,1.5481537353,0.8036272576,0.1390521327,
0.0001405348,0.0011494220,0.0045166867,0.0094978101,0.0306218080,0.0939856157,0.2357204450,0.4718046138,0.6116351769,0.2999876844,-0.2711299002,2.7606241881,5.2101943939,-4.7229763526,3.7918291376,10.1148570577,9.2644631861,-6.1638971329,3.4350109751,9.3209561993,6.5326356802,3.4307484952,-0.0060429651,1.3497298654,0.1939373747,
0.0001759841,0.0013001060,0.0020404017,0.0081096109,0.0318453927,0.0995228623,0.2723109255,0.5681195478,0.6727570500,0.1140268712,-0.3681602727,2.4374987156,5.5292883413,-5.1664325865,6.8373690989,15.7508885727,1.3539817398,-6.9301876397,6.4274320364,9.4822604248,5.4053750303,2.2141059974,0.9979941146,1.0559612841,0.2024163907,
0.0001561735,0.0011399779,0.0025351189,0.0088207216,0.0351904199,0.1106356534,0.2846283801,0.5527087793,0.6325525446,0.0904587570,-0.2892017581,2.4841977541,5.4564752261,-5.5360724426,5.8162008806,16.1177481401,2.4869534341,-7.5724088445,6.0478655179,10.0497792329,5.4992116731,2.5770774616,1.8129304467,1.1338915064,0.1965252455,
0.0001196368,0.0008950624,0.0029376058,0.0078161530,0.0092336639,0.0321456176,0.1225309514,0.3318026363,0.6360816274,0.6581806702,-0.1730169678,-0.3852560192,2.6082681434,5.5401655371,-5.5660906831,5.1263977285,16.4860721155,3.8324278333,-8.9682743063,3.6573329478,11.1820074159,6.7739858461,2.5465742504,1.5691136660,1.6673831128,0.5777543401,0.5768316629,0.1465797518,
0.0001056741,0.0002824484,0.0010400285,0.0056711807,0.0202656005,0.0532673594,0.1248029828,0.3017033748,0.5740931849,0.6052616966,0.0106798541,-0.2461425832,2.6581342114,5.3300520221,-5.3806805558,7.5267394203,15.9699381393,2.4755905706,-9.7192666029,9.1570913303,8.8760722595,2.5683311761,2.3892827718,2.2433430737,2.3799598613,1.1419568274,0.7742604659,0.1581642274,
0.0001036964,0.0005194857,0.0007140172,0.0046418233,0.0151798038,0.0445846249,0.1306225873,0.3332213894,0.6110253619,0.5672136623,-0.5062619486,0.5921293456,4.1366991702,4.0182175933,-5.2602112702,0.5438008388,18.0316935081,8.9084062159,-11.8771609764,11.0842245422,6.5209595914,5.0612406816,3.7717715320,-7.2269533866,8.5155672303,2.1570477675,0.7037825385,0.1172205742,
0.0001301061,0.0010358972,0.0002149741,0.0048854306,0.0047725656,0.0196338674,0.0676882130,0.1903622422,0.4416406567,0.6949911192,0.5917519846,-0.5247193623,0.2276066181,3.3381164024,4.5401918012,-5.6079429169,6.9511634478,17.4698983150,-13.1052944810,7.1113223736,14.4553498131,5.4009578222,0.6666858639,1.8868627570,2.9470667862,2.7692406281,1.3058095916,0.1505774833,
0.0000865301,0.0005119142,0.0017444460,0.0049412325,0.0100081435,0.0370619493,0.1221738603,0.3302135074,0.6432463803,0.9974906399,-0.4802990430,-0.1601838422,3.5085503233,5.3243199942,-2.2333971788,-4.1749179672,15.8671528243,11.0216242148,-11.8476001267,2.9319300015,15.3521174263,6.8480235393,-1.8128763207,2.9611959944,4.8266137433,1.9474810205,0.7649896958,0.2077970976,
0.0001204631,0.0008619213,0.0001844362,0.0043732341,0.0134274090,0.0389131135,0.1134304884,0.2829315551,0.5358760570,0.6243914157,0.1548369840,-0.3283423236,2.2910024635,5.5867339364,-9.2841710053,7.5779591757,21.1919021088,0.7060025027,-12.2200713578,10.0126204066,12.7359595926,2.5115260446,-1.0338463421,4.5059823307,3.0375468021,2.8090198729,1.9103538343,0.2204748807,
0.0000881860,0.0004503310,0.0003513143,0.0028420245,0.0079960537,0.0209214016,0.0634946365,0.1790313051,0.4128564627,0.6600652434,0.4789669054,-0.3126672943,0.0328501600,3.0844314049,4.9620525129,-5.8833821140,5.9885860731,15.4724355216,5.9853108579,-13.1318143095,17.4758669776,10.1546655375,-4.0622398230,2.7674343699,1.2312538217,6.1161480484,1.8981671217,1.6262389080,-5.0065955141,3.9890619558,-0.0083908807,0.7935228005,
0.0000782039,0.0004275544,0.0008032103,0.0023209281,0.0025678649,0.0115113013,0.0273081860,0.0867980934,0.2388372833,0.5049916271,0.6691584195,0.2186254577,-0.4566584038,1.2139728553,5.2197051349,2.3876545643,-6.4826589023,3.6512790691,20.8829225582,10.2710531610,-21.5887613705,12.4760051822,13.1372151325,-1.0881848436,-0.1665617735,7.8298141730,4.4933622397,-0.4583111913,0.1817142270,1.5835392653,0.7307186472,0.4187521457,
0.0000723789,0.0004107311,0.0008083013,0.0013814634,0.0030253719,0.0138514044,0.0389115639,0.0892191133,0.1678096632,0.3130568105,0.5312182852,0.5322543703,-0.5223963197,1.4659052986,5.5995366964,4.0593097683,-8.0577295088,1.4232188292,20.6100478974,9.5312068251,-19.0684418680,13.1090776981,12.4855035785,-2.3698425993,6.8783750594,2.5625264381,3.7437621981,0.0391720843,1.0899160242,1.4054750081,0.8727601235,0.4505973114,
0.0000758769,0.0004586389,0.0009803635,0.0038275240,0.0122996066,0.0204256772,0.0516169634,0.1569558354,0.3702517660,0.6343622267,0.5652475130,-0.2337097532,-0.1158181502,3.2430077299,5.1276997683,-3.1908876786,-2.8736166747,19.3973590373,8.5005859472,-16.0043939156,7.2940203340,18.9032734983,1.0346270047,-4.0610315782,9.5832472394,5.7280731597,0.8168535940,-0.8736023753,1.5121304058,1.9084839962,0.3162533033,0.1709431161,
0.0000884685,0.0003140552,0.0006745632,0.0036932855,0.0101201746,0.0179067517,0.0565426766,0.1608519159,0.3703119837,0.6124697160,0.5186870267,-0.1046648754,-0.1656281540,2.6193608140,5.3313408009,-9.8221405155,6.7776610963,23.0677502032,-0.8047380834,-16.2633473248,11.7806640474,18.5729481030,-0.0143659378,-0.4469343107,8.8898978975,6.4685556762,-2.0484406561,0.0683622840,0.6605461950,1.5488273433,0.7870707467,0.3456140327,
0.0000845944,0.0006241972,0.0002738029,0.0022768567,0.0048181146,0.0155316583,0.0444340719,0.0736597236,0.1505044473,0.3845872776,0.6493185613,0.7070860097,-0.4517977197,-0.4056705742,2.9242120578,5.4268609395,-6.4504216265,7.9904851327,18.9032811188,0.6583633777,-14.9211788286,14.4036897915,13.3325986951,-2.3930489441,4.1072684517,8.1366945987,4.0587301357,-0.6764936582,0.6925305515,0.6950508112,1.5197225205,0.4159238533,
0.0000872348,0.0004656745,0.0007405672,0.0036308328,0.0096717699,0.0161771248,0.0483191402,0.1367570779,0.3313026177,0.5940521842,0.5728516116,-0.0414755022,-0.2099964274,2.5195865840,5.4391250454,-9.8880172880,6.6767809098,23.1313243425,0.3547430156,-15.1831158230,13.0950699320,16.0696003272,-0.2294841094,3.4188898896,6.0437056146,3.6367035217,2.0095787070,-1.2455089715,1.1788171888,0.6372067249,1.4933057094,0.3791047736,
0.0000777491,0.0004752696,0.0008292112,0.0035550472,0.0100829781,0.0154320655,0.0526563885,0.1477627256,0.3393417887,0.5880360065,0.5622743788,-0.0749892576,-0.1553766288,2.9578444305,5.2101698317,-7.0933472448,1.7281386370,22.7989912724,8.2241354391,-20.1474008369,8.6765004004,19.1302329379,2.0325320310,-1.3142838881,8.1883990364,5.3864393116,2.0456325526,-1.4906661888,1.7450298874,1.9107270899,0.0779043244,0.4428632539,
0.0000911053,0.0006152500,0.0004315440,0.0040522904,0.0148100004,0.0039657469,0.0506540276,0.1483875648,0.3530405003,0.6184462734,0.6006411074,-0.1315040329,-0.1903191788,2.6003343871,5.3854233698,-9.0387299180,5.7140651717,23.9082703759,-1.5732126321,-49.8876309356,42.8352108971,21.8446587473,3.5481516992,-4.3006680023,9.8803658704,6.8346754725,0.3881245341,1.4058714016,-1.6580384525,1.9890701104,1.3711658682,0.2795798361,
0.0000854049,0.0005347673,0.0006363041,0.0033959537,0.0095836865,0.0184143827,0.0519385596,0.1408326404,0.3218560389,0.5680557016,0.5801602559,-0.0308194872,-0.2488111079,2.4417585962,5.5971001311,-7.3666949876,4.7934582983,21.9790013138,3.7570428049,-17.1083464589,18.5295144692,11.7165997909,-2.3062081701,3.8458596950,7.8338993987,2.7100181838,4.6072989388,-5.9331298394,4.7492066101,0.8827216045,1.5114306927,0.3436058272,
0.0000845193,0.0006067711,0.0018600691,0.0035873863,0.0098499043,0.0204497772,0.0598109964,0.1612597313,0.3620779806,0.5996844247,0.5298101578,-0.1256678384,-0.3002580427,2.4141405679,5.6576673255,-7.9413352898,7.3221348764,23.3606576214,-6.5846205217,-34.1607310737,32.1670628548,20.7599142806,2.6838804413,-1.6508075419,9.0383423947,6.5262960207,0.9388255554,0.3235902617,0.0250552283,1.1779187724,1.3282273415,0.2906250474,
0.0000801936,0.0005824305,0.0015676176,0.0028480739,0.0099143124,0.0185725852,0.0516596631,0.1484530023,0.3498749833,0.6068543033,0.5520149751,-0.1407844266,-0.1369362591,2.7869200875,5.2896128989,-7.1663887602,5.6134623439,22.5168555592,-5.3340080152,-28.4757408096,26.6063589732,21.4677443811,6.8074582597,-5.8123285842,9.3337945708,6.4120354414,1.6697682418,-0.8180721442,1.3772941802,-0.3251163072,2.1502385962,0.4354096320,
0.0000848094,0.0005894225,0.0013760235,0.0034732601,0.0131549581,0.0335667866,0.0520705296,0.1225000550,0.2987154449,0.5484095507,0.6018498896,0.0154626556,-0.4697715697,2.1654343556,5.9190105612,-9.6597153961,8.1908033981,23.2976467257,-8.3813112803,-42.5694362540,44.7306384096,20.2817200428,2.4562656606,1.0943417102,7.7602944298,5.7866389781,2.0068750920,-1.2722976282,1.5557186531,0.4729149147,1.5773616353,0.3656141758,
0.0000760994,0.0005849677,0.0004797042,0.0026026504,0.0102598686,0.0269785678,0.0574795477,0.1411532084,0.3271721835,0.5760436802,0.5743717574,-0.0460376734,-0.2059393077,2.6852111066,5.4324520169,0.9083261762,-7.1745427789,19.5939249755,8.7681830693,-17.9634645705,4.3325552399,22.5657642081,7.5250155061,-0.8322709484,7.6071145754,8.1361169761,2.1009462907,0.7121341687,-1.3817701223,1.6085311190,1.6094403673,0.3011073703,
0.0000855967,0.0005528472,0.0004219822,0.0036546669,0.0112510939,0.0159534244,0.0509694702,0.1502011663,0.3548317924,0.6190796180,0.5712115222,-0.1610362873,-0.0532036906,3.6066034910,5.2266482798,-4.0084309576,-3.6005446005,21.7175825616,11.5380870038,-20.5085283001,5.7712452838,18.8239461850,8.1646659044,4.2835189997,6.2576307158,4.7937358920,2.4783912071,-1.4352792485,1.9301550475,0.4342438955,1.6039056143,0.3584498227,
0.0000758138,0.0005663788,0.0015851888,0.0019655893,0.0108049814,0.0331536550,0.0876379176,0.1861679724,0.1354531696,0.3676032588,0.5648712538,0.3528686185,-0.2625630059,1.3922390530,4.9030554901,2.5054852750,-6.8167277552,18.0491040840,9.4512905115,-15.8167054035,19.8058848258,13.1425548480,0.2704297218,4.5899831288,4.4999509098,5.2606418674,4.1986369974,0.0890116679,1.0764130000,2.0506647243,-1.2165273373,1.0844235995,
0.0000719787,0.0005272670,0.0017347560,0.0031667947,0.0114240708,0.0342588648,0.0877425913,0.1742167327,0.2173512327,0.4255783199,0.5975105535,0.4305113518,-0.4414933627,2.1311772493,5.2151884459,6.5251788069,-11.7319108092,22.7884570415,5.9688723617,-17.8407348595,14.8888305613,17.0794782501,3.9492557958,-0.7870028380,8.0936187948,6.4900155777,2.7293691027,3.4068664826,-8.2169050663,7.3935076364,1.2563219338,0.1178143813,
0.0000634594,0.0004594791,0.0017490479,0.0048123528,0.0123110825,0.0259050438,0.0585520607,0.1461757882,0.3205816138,0.5571176514,0.6755314334,-0.1123484803,-0.7025575156,2.0947919359,4.2911810878,2.3056207575,-6.6360954680,13.3897818535,13.8597155367,-16.6810915550,13.5718953719,19.4498162460,2.6365587680,1.5460578202,9.0202711399,6.0180569125,1.3217282682,0.9322390397,0.3674843581,2.1474510932,1.2467963860,0.1293874307,
0.0000703567,0.0004770623,0.0017534287,0.0046170085,0.0076778799,0.0184040516,0.0523094617,0.1302107366,0.2841072966,0.4773744285,0.4546716511,0.2932094241,-0.1867074785,2.6200470780,5.3628556909,-9.4784316725,4.3371717204,23.9935293661,1.8359967401,-20.3652547166,11.6265198239,25.0593570645,6.4843355460,-11.2976831879,17.0471832778,7.6546484311,0.2848481333,1.7699445326,2.1553646241,0.6502270147,1.4837377206,0.2374275050,
0.0000638224,0.0004254248,0.0010620256,0.0024386530,0.0079967742,0.0224333297,0.0613626239,0.1575967396,0.3527518128,0.6031336785,0.6173760238,-0.1613570242,-0.1955549739,2.8081431686,5.4045656072,-5.8549322798,-5.6579598978,14.2325280466,17.9315736630,-17.8234612008,10.4858919836,23.1212918199,4.5872456532,13.7539827129,-6.6217723273,8.3158637255,2.5353103407,-1.4943928086,3.3379599077,1.8623155381,1.3488785295,0.2572389077,
0.0000597259,0.0004673893,0.0019249492,0.0021010055,0.0070189239,0.0225894758,0.0585354528,0.1396519145,0.2907249674,0.4544658228,0.4211540223,0.3410622750,-0.1567462331,3.1316727732,5.4192283800,-2.7563873716,-5.8499824903,14.7794022002,15.4693766388,-17.9132858616,2.7564678328,24.2473485992,9.7200865386,28.9746284294,-51.2472892134,38.1296181701,9.1514959444,-11.1602497408,8.0045571968,0.1406460365,2.1271799869,0.2924762595,
0.0000569513,0.0003331661,0.0008888839,0.0020150524,0.0052356941,0.0166766426,0.0494050656,0.1301582831,0.2527870818,0.0494651131,0.5363301002,0.6033430211,0.1082546852,-0.2610891876,2.1876967772,5.6655785480,-18.6854268105,14.5230085806,24.2071669965,13.1349944158,-29.1710884277,19.5389481832,16.9128506332,1.3989325424,8.7571973696,4.3449698848,3.5185963226,0.7935460685,2.7576235204,2.8369893083,1.5486859982,0.2358695362,
0.0000669910,0.0004506671,0.0004835830,0.0019871333,0.0061912741,0.0151842589,0.0391912783,0.0916700640,0.1785521942,0.3272631137,0.5425312367,0.5495635589,-0.0594440940,-0.1996613412,2.5773003384,5.4808887175,-6.8470080588,7.9330565663,19.2868459415,-30.6507877629,11.7819907294,7.3968293938,27.4229226169,5.1938547985,9.1566181552,8.0480780036,-2.6594832243,5.0648053953,3.4760646898,0.9766263837,1.5449542643,0.3224131339,
0.0000536582,0.0003416086,0.0011470539,0.0016198573,0.0030448773,0.0124249145,0.0347141262,0.0824973536,0.1736253299,0.3371640132,0.5416530253,0.5329171356,-0.0223255772,-0.4123275052,2.2419396262,5.7949867173,-10.9761193377,7.5462996831,24.3539740020,0.6507513055,-19.1655918847,17.1718381385,21.4745790624,0.9272522110,8.1421275456,6.5597834990,0.6696909463,5.0330447036,3.9272387814,0.2298238291,1.8221460293,0.3096852709,
0.0000540017,0.0003628577,0.0005474506,0.0019635331,0.0070511353,0.0178792921,0.0327805892,0.0672026408,0.1626839229,0.3382335962,0.5509495128,0.5453274980,-0.0219734251,-0.3919240885,2.2190509435,5.7658746523,-18.7375974773,15.4118923565,25.6060989062,-4.4503964906,-22.5912465448,16.4404434387,26.3179840627,4.1645265492,-5.6078111213,14.5531219042,8.5925498615,4.6060970912,0.8326506271,3.0182897846,1.3552401951,0.1920927447,
0.0000558991,0.0003819901,0.0010307052,0.0016056774,0.0057067566,0.0147858883,0.0386272501,0.0919715066,0.1823598766,0.3233728054,0.5224676816,0.5492314567,-0.0255320544,-0.7241076495,2.5155648978,5.8547636404,-7.8730434810,6.5669726090,16.5732560501,6.6152042075,-19.3322225527,23.6388441301,16.9879473971,-1.9019686778,3.7465709811,7.8594098977,5.9485735483,5.1041659166,4.1718164225,0.0032970471,2.1934434348,0.3454467416,
0.0000493289,0.0003684282,-0.0004229149,0.0019746103,0.0051623503,0.0072442638,0.0172784360,0.0058349597,0.0570490879,0.1536748415,0.2759299926,0.0935923714,0.5618579879,0.5463014038,-0.1152918146,2.7554309581,5.1947076257,0.6525415255,-7.3681190490,18.7777925197,9.7218369548,-20.9404518756,2.1805037737,18.2644236314,21.2667564719,-1.4594238812,10.2691810340,7.4801579967,4.9265836185,4.3921589102,-1.4000085364,3.4936306797,0.8334492422,0.2502464946,0.0979985729,
0.0000464989,0.0002906478,0.0006415166,0.0019052013,0.0041414378,0.0068544320,0.0201492994,0.0391797115,0.0912058330,0.2128874770,0.4138489080,0.5818088056,0.3980189474,-0.2181904180,0.2694315604,3.1042861394,4.7078475094,-8.6279399172,2.5349545474,24.9288201053,25.4311955895,-42.4989198055,18.8011484591,21.9460208567,-2.6015628854,11.1073236910,7.9257134199,2.9529378402,3.4742334211,1.6558456933,2.3299740425,0.8252827453,1.1874677020,0.8261074613,0.1670435261,
0.0000431027,0.0002706534,0.0004911032,0.0008480109,0.0024756596,0.0073502468,0.0199890721,0.0079221312,0.0510838556,0.1250316214,0.2485825124,0.4230278622,0.5605697777,0.3986418546,-0.2179099698,0.6127772623,3.0173818221,4.4099205807,-9.1416308957,3.3393704052,25.9202521610,10.4793382691,-32.9404293375,12.8889959310,31.9647602285,-3.0240212747,13.0047259823,-0.0888115753,10.6039424986,-1.3065156622,5.3879378821,3.7561217772,0.2221537184,1.9172784452,0.3480342879,
0.0000415907,0.0002792605,0.0009489266,-0.0001057597,0.0022961215,0.0062180817,0.0156239653,0.0288998213,0.0423024061,0.0974123953,0.2111022017,0.3961722005,0.5637519373,0.4169777325,-0.1796134901,0.0842181549,2.7461891902,5.0604771411,-9.0287636386,4.2586727374,25.6623152813,-33.6793326197,15.5124728618,19.3245073955,21.3885922321,-5.4862084346,10.9753593787,11.0105827706,3.4025575085,2.1686311504,2.5645358328,3.8047789101,0.0755177692,2.2008358292,0.3517531580,
0.0000560258,0.0005429502,-0.0004062117,0.0014202315,0.0013744770,0.0064260115,0.0183813687,0.0163859821,0.0331177496,0.1100833131,0.2354022909,0.4294622417,0.5844041172,0.3894369025,-0.2320596317,0.0919422844,2.6623931651,5.1096663420,-9.0179918738,4.8209010248,25.6248248371,-21.2404831739,-0.5779879762,28.2034371470,22.0591911559,-10.8448412996,2.3107601365,15.7307856030,7.0946981819,-0.2353234100,4.4619279440,4.4836723849,0.4831305807,1.9532132603,0.2320558674,
0.0000399620,0.0002794999,0.0006170736,0.0006157445,0.0027865034,0.0023744359,0.0056249785,0.0161182231,0.0427300191,0.0928342502,0.1432818205,0.2150359426,0.4166157385,0.5520809003,0.3842952993,-0.2204476705,0.5208368840,2.3219927010,5.0342709846,-7.1809207055,17.0471987826,13.8512052071,-18.1651487330,-6.1733621592,33.0035798537,21.9793190307,-15.7126022080,13.0510071404,7.6702271652,4.1059622043,4.3025103342,5.4282639414,0.4345272501,2.5023852408,0.3238643645,
0.0000401814,-0.0000531474,0.0001358853,0.0000083703,0.0003887638,0.0005482065,0.0016170997,0.0028163698,0.0069449908,0.0158756442,0.0237378715,0.0529155053,0.1125755469,0.1807307127,0.2843475187,0.4659250233,0.5102671124,0.1267951341,-0.2088391687,1.6356780735,5.0746039779,1.8806650040,-7.6105698948,4.2274663638,24.0477662910,0.7435652441,-24.0259304421,17.3301589081,29.9701078415,-3.1133713233,-5.9008314802,16.2499601426,15.6209801756,-10.9553805698,9.7669167659,-16.6891927041,19.1384541346,2.5721142612,4.7542104405,-4.0365677891,5.5406177815,-3.2649640389,2.3719752942,-0.8843698612,0.9791597825,
0.0000219421,-0.0000215240,0.0000938711,0.0000308860,0.0002837665,0.0004729035,0.0012204902,0.0023021564,0.0055120380,0.0131599339,0.0218112687,0.0465200965,0.1069821525,0.1997325287,0.2850183859,0.4041538929,0.5194286876,0.2365460237,-0.3280279725,0.8220471365,4.6365097940,3.2575216782,-7.8053194478,1.4226479116,27.2364060520,-1.7029401003,-26.7328113150,19.3368654200,36.5932719788,-7.6452456512,-7.4666923991,17.0914830434,11.2019409392,-0.4317128368,1.8336661793,1.3169083301,8.2304500365,-2.3995114573,9.1956334905,-8.7702092086,12.2154524929,-14.6925953854,11.5764074326,-3.4203111613,1.5848955196,
0.0000261606,-0.0000506346,0.0000996816,0.0000353311,0.0002370657,0.0002530887,0.0007304550,0.0018263460,0.0048693627,0.0079649658,0.0159294307,0.0367664010,0.0699184179,0.1231971566,0.2185021829,0.3195824004,0.3843381860,0.4651930178,0.1612238552,-0.3302949459,1.0992951959,5.1416684401,3.6066703920,-8.1498930491,0.0021458892,27.0869942396,5.5736437077,-30.0934656109,14.1548174322,35.1307767213,-10.8809096598,2.7694415751,15.2827086792,9.1138482973,-0.0714348184,1.4283722907,6.9954935456,2.6413688983,3.5947866092,-2.7547484779,2.4195162602,0.9077318430,2.3506619739,-0.2073891403,0.3775508407,
0.0000254130,-0.0000289764,0.0000779674,0.0000361448,0.0001969290,0.0003505837,0.0007106883,0.0014807288,0.0049342540,0.0075119283,0.0142111408,0.0357849130,0.0659705170,0.1166443155,0.2089169789,0.3222744044,0.4230190552,0.4570813867,0.1475877244,-0.2826635150,1.1375799532,5.0425521580,2.9676530466,-7.8775513924,1.1055516294,26.7243628444,2.1234357349,-27.1241572761,14.8814104549,34.9896522763,-12.2899694859,2.6590634158,16.6409478573,9.5558585396,-2.2096138513,2.9616055287,8.0960919936,1.0698109272,3.7486063072,-3.2545816829,3.6646689055,1.4984914811,2.7137842353,-0.7748969008,0.4255207188,
0.0000212980,-0.0000226844,0.0000843508,0.0000411916,0.0002751931,0.0004824088,0.0012211377,0.0022561174,0.0050860258,0.0128372990,0.0223487625,0.0464532400,0.1089839020,0.2073867072,0.2867993860,0.3927043772,0.5104203343,0.2378488486,-0.2975809670,0.7400868731,4.1740872149,3.4430687964,-8.0131720952,2.3783312911,27.3115584239,-2.3263430292,-27.7990193746,19.0780078861,37.6782501154,-9.1293254390,-7.2466139796,19.7361073154,11.5202979087,-2.5296228160,3.1409961613,1.7252577956,8.6745825045,0.4018315144,5.6748383229,-11.7697533374,25.5960673364,-28.7454953643,19.0338265062,-4.4152523572,1.1297548979,
0.0000182264,-0.0000152218,0.0000705259,0.0000629002,0.0002878211,0.0003235088,0.0012443861,0.0031999852,0.0058681300,0.0101126873,0.0250687168,0.0455342230,0.0841584166,0.1728432170,0.3051140511,0.4448520074,0.4952348891,0.2573922813,-0.2056160007,0.6994520759,3.7429838802,3.7401820998,-7.4729194091,1.4336362034,26.4256536997,7.8432243587,-31.2155459982,22.6405740284,28.7043532500,-8.0569250833,-7.3240605694,17.8171500586,10.8559729389,-0.8828358253,1.9959185275,4.6548862499,10.1866345791,-2.9499368062,7.6408655340,-10.1585098285,39.1601333438,-43.5861015934,15.2204173442,-3.5896638367,2.8287060271,
0.0000436313,-0.0000796134,0.0002110689,-0.0001466851,0.0002921836,0.0001785149,0.0006819194,0.0005938105,0.0025280553,0.0029049938,0.0074028476,0.0142005920,0.0281175342,0.0546865758,0.0779202122,0.1236319965,0.2670626611,0.3932173733,0.3797884386,0.3835183667,0.0426359729,-0.4950507826,1.8188788879,5.3199865230,1.4182630873,-9.2984580039,4.6332733665,26.9727399569,-6.5307314790,-21.7706346559,22.8774375019,31.0664345699,-13.8866676293,6.7589012703,17.2220505802,3.3873522755,2.1719299647,9.0831652899,10.0040913581,-5.0643016393,1.6698194824,1.5331229795,0.5884054096,1.5207730255,0.2198282110,
0.0000228664,-0.0000301588,0.0001376541,-0.0000767520,0.0003503881,0.0002519175,0.0009477172,0.0010517557,0.0029891637,0.0073651519,0.0092822113,0.0207274780,0.0479199333,0.0943987060,0.1563914949,0.1864411131,0.3217675762,0.4782665806,0.4202277059,0.0503144389,-0.1170602743,1.6341331552,3.8450197437,2.3604578133,-9.4454185779,4.2154048399,26.3218444527,2.4218739755,-26.8669306565,30.6568972855,24.2352923527,-15.5237430327,0.2218038673,20.7731455734,5.7642351928,-0.6655845178,7.6406989629,7.2587051141,2.9765160154,1.0318414657,0.0816743826,1.3068324722,1.3321098435,0.6016183940,0.1398852149,
0.0000156999,0.0000010015,0.0001030603,-0.0000377345,0.0003271234,0.0003184375,0.0007859768,0.0013248548,0.0032795809,0.0087311460,0.0091288027,0.0175175737,0.0459842239,0.0883250900,0.1564236093,0.1913070923,0.2595061334,0.4705405859,0.4679419154,0.0796750432,-0.1520001772,1.2742400627,3.2582729259,3.3429255857,-8.6680623810,3.1203888201,25.4636239517,3.2354313291,-26.9219269692,25.3414080332,28.2268403181,-13.9800800217,-0.7798379795,19.9955006954,7.4021562150,-1.0853914581,7.6856476361,8.7985564804,3.5159467506,0.7833580322,-0.3877852123,1.3950864504,1.6765863394,0.5772092848,0.0807060718,
0.0000235562,-0.0000294574,0.0001324952,-0.0000670362,0.0003475707,0.0001102610,0.0010396549,0.0007686728,0.0033169918,0.0085537985,0.0074019946,0.0168924894,0.0406771970,0.0814925619,0.1493943619,0.2255908650,0.3182000053,0.4361737229,0.4202903156,0.1036874515,-0.1704353560,1.0427186792,4.1240553235,3.1498850070,-7.1313213300,-0.0196399416,26.1165228982,11.0970920332,-33.3249914457,39.0419020015,21.9502193791,-22.5431261047,3.9038436168,18.3850989190,5.6837077277,-1.4689016642,10.7364843569,7.6768983751,0.4171853515,2.4155914740,-1.7728934725,2.9525536556,1.5294959023,0.2679086685,0.1261484729,
0.0000247142,-0.0000260814,0.0000878971,0.0000752826,0.0003000174,0.0004046534,0.0014683214,0.0035676679,0.0059511777,0.0107339749,0.0278665946,0.0602717870,0.0936956463,0.1411681724,0.2951184156,0.4758443248,0.5221596193,0.2085513381,-0.1486416982,1.2529730488,4.2166530318,2.5870998979,-7.7380866854,2.6927128527,26.4006237940,0.6005111078,-27.2381959139,30.5844041814,28.4286010907,-17.3181693740,-4.0017607735,18.5859324156,10.2365769024,0.9865871114,4.8783832536,6.1618434476,7.9548223325,0.2656155269,8.1896257380,-15.2912662183,17.6404994702,-8.8168363418,5.1319391974,-3.4113454843,2.3216345654,
0.0000216752,-0.0000159842,0.0000772789,0.0000916944,0.0003371217,0.0002950145,0.0015627342,0.0038782935,0.0060986158,0.0113290406,0.0280797308,0.0546531243,0.0861348069,0.1580715827,0.2965433970,0.4623434463,0.5157927638,0.2259057533,-0.1423160895,1.1388454306,4.2614065392,2.9074393092,-7.0816542918,-0.1912387401,26.4037308587,8.4944038732,-32.1859863789,26.6431564095,27.6690532145,-16.7277618506,2.6380089988,16.7748127260,8.6050730992,0.7967132718,4.6712907327,7.4351954845,7.6147868623,1.1377862642,4.9559698648,-15.1843372209,21.4251752780,-9.9433029029,4.3249048699,-1.2050921241,0.9127364219,
0.0000186609,-0.0000138993,0.0000803616,0.0001108991,0.0002932068,0.0004381580,0.0015661273,0.0038982080,0.0066071654,0.0106523897,0.0265275364,0.0565076127,0.1042909358,0.1673541915,0.2747580037,0.4311381317,0.4943555900,0.2568996921,-0.1307111351,0.4227817335,2.6846433200,4.5708947307,-8.2802091730,3.5102191456,25.9707354183,1.7333589014,-27.8790966284,26.1829629571,29.0945534302,-19.9443507288,6.8411241907,15.7805647106,5.5882010838,6.3444120021,-0.3199386500,11.3342730370,14.7610403443,-8.5740052787,12.0869876523,-18.4467159680,19.2177662991,-10.1012429435,4.7763523055,-1.1616640834,1.1015803553,
0.0000180615,0.0000045381,0.0000903870,0.0001463201,0.0004471196,0.0007126872,0.0017938242,0.0051994471,0.0109222113,0.0216892844,0.0439416956,0.0850978292,0.1540675127,0.2686055910,0.4269627121,0.5191870802,0.3177878844,-0.1108387417,0.6335459318,3.5052633359,3.9479697996,-5.9495630613,-1.9195224345,23.9181076419,9.3779220344,-29.1650362222,40.5838508023,12.7398670004,-19.5301637867,7.8090594918,15.9706122384,8.6346158979,-4.0137993017,9.9352442643,19.7784002980,-12.0950428671,12.6831223284,-10.0937039190,32.0767136925,-36.1204877428,19.2529916770,-10.9250052192,8.0745061179,-2.3881224498,1.5328190079,
0.0000164574,-0.0000055485,0.0000697511,0.0001040496,0.0002934148,0.0005296219,0.0017984526,0.0043318803,0.0062514124,0.0129488690,0.0296183494,0.0520749272,0.0895519541,0.1694593318,0.2917252124,0.4341113260,0.4942471604,0.2619013973,-0.1055503639,1.0298815390,4.3298910498,3.2275364729,-6.5167619594,-1.4052853242,26.1345544364,17.5719053915,-40.3667394794,27.6988907559,26.6881533298,-14.8133680626,-5.9616760776,21.8647911528,11.2769358795,2.4441759303,9.0667532324,2.7445721878,8.9789066396,-0.5169714727,9.3223521469,-20.6337695655,40.9816880695,-29.3148191104,5.5409815399,-0.8378441050,0.7217877476,
0.0000132787,0.0000099434,0.0000636579,0.0001478655,0.0001945675,0.0005757016,0.0017712476,0.0041123221,0.0065403185,0.0109698261,0.0276976153,0.0562371903,0.1014741063,0.1712801208,0.2823019652,0.4238409850,0.4861818478,0.2725898129,-0.1260613466,0.7713662286,3.7646648012,3.5933318520,-6.4180147375,-0.9633431265,25.7819597220,13.1152397346,-35.7574180653,8.6409927242,43.9285820332,-17.9527877718,8.5627647040,13.3859790321,9.9829503965,3.9956548100,7.9034299114,4.0013879211,8.3670780331,0.0409430758,6.5841170994,-17.9219920686,26.1566135322,-14.6932611811,5.1067812444,-0.1435202736,0.4465593430,
0.0000142959,0.0000291353,0.0000955181,0.0001652527,0.0004172095,0.0013442949,0.0017416525,0.0040524318,0.0103689333,0.0214623373,0.0421141180,0.0794789596,0.1482469992,0.2678265923,0.4278629182,0.5171208308,0.3227982622,-0.0736149951,0.8944645445,3.9682794120,3.4858704690,-6.0410938169,-1.8909860771,25.7893595036,23.5692077822,-45.5532027449,35.5845105182,18.0497796578,-18.7816354173,3.0803796153,19.7887933953,19.0645203486,-12.2227784067,13.8695259279,11.0582323839,-0.0970653522,11.8040790008,-27.9310799379,60.9435616593,-65.6821619516,27.9758689691,-3.4013807520,6.3573638434,-2.7803848317,0.3264475111,
0.0000140173,0.0000267494,0.0000778951,0.0002963638,0.0003838090,0.0009371620,0.0024553449,0.0054310573,0.0099925777,0.0194799208,0.0452363260,0.0941060263,0.1717848744,0.2801480865,0.4054282520,0.4776624918,0.3414641063,-0.0394411109,0.2272598889,2.5635799371,4.7068520151,-7.4523077247,1.2741986023,22.9792681764,8.0276930810,-28.5614996692,44.3620623399,8.7413964505,-25.3669036551,17.3457942681,18.7310978891,-1.9291103257,10.1867209331,3.2875299565,11.4686041434,0.2868966251,7.5146342095,-4.4264374704,6.8083454697,-7.1631860105,14.7531659101,-12.7114082231,7.3204523959,-1.1571212279,0.3669380653};

	static constexpr double alphas[2919] = {3.940884339,1.795656395,1.002441646,0.6043669349,0.3748873204,
12.74592889,5.838560713,3.298353782,2.035960835,1.309047068,0.8575669916,0.5605551204,
18.6745246,8.523633889,4.803141306,2.966947857,1.921618804,1.279100511,0.6552675507,0.476213702,0.3150022159,0.2130277588,
26.37061737,12.08854508,6.905435588,4.351167231,2.887484259,1.975332302,1.054161021,0.5848741386,0.4116218738,0.2864269505,
39.01953916,17.96361129,10.24467435,6.390688149,4.191618979,2.836715303,1.974161177,1.288805151,0.9210849635,0.6305555392,0.4276367723,0.2704236528,
46.82882203,21.45346794,12.26783452,7.683842738,5.061359613,3.439256268,2.313316158,1.760399338,1.068769816,0.7461930441,0.5059030154,0.325481024,
57.42557427,26.39062095,15.13869145,9.474109608,6.222353863,4.228453789,3.02480095,2.203560009,1.277162141,0.8828621166,0.5945404982,0.3834347141,
74.58514575,35.81973256,21.69737298,13.88069386,9.170094583,6.256795145,4.390235388,2.680016775,1.615741907,1.216801204,0.881368394,0.6124328094,0.4088961335,
82.76111007,39.76086361,25.4373533,16.64366659,10.91026631,7.369039238,5.119103896,3.163125578,1.801547016,1.306308036,0.9387578207,0.6595990661,0.4481481262,
93.50933383,42.86115608,25.4933612,16.70048962,11.38567231,7.957132554,5.665772119,3.658422705,2.057654937,1.476304449,1.044137447,0.7225524631,0.4873077539,
102.7074314,46.7371368,27.96967728,18.77916533,13.08042496,9.185110154,6.49308209,4.072052119,2.264725043,1.598181895,1.127094193,0.8120651723,0.464881501,0.3103287837,0.2106548955,
119.3584012,53.26804284,31.69387742,21.01570871,14.31818496,9.938848874,7.029972698,4.795500881,2.507120745,1.774481938,1.253602543,0.8121008496,0.5474358483,0.3911641254,0.2703831041,
118.3434893,51.00947448,28.40020653,17.6427734,11.66866906,8.034064133,4.551165325,2.827135447,2.043229503,1.478674221,1.038911199,0.6306633095,0.4895271913,0.3384510733,0.2177269919,
131.1334311,55.97841065,31.00155064,19.22453814,12.70255972,8.741565132,4.949233475,3.125682442,2.292311442,1.682893022,1.182647097,0.794165943,0.5977210018,0.4098975592,0.2690280357,
148.3710024,62.0839976,33.87213795,20.77441148,13.63189862,9.364760519,5.511751456,3.535177567,2.723268375,2.055843818,1.090840836,0.8928899221,0.6307114538,0.4436416132,0.3018908445,
162.6947928,67.88819204,36.98583249,22.64507463,14.82808238,10.15596523,6.010295044,3.671828807,2.769101874,2.122479709,1.426272066,0.9302531182,0.7149683119,0.5075068601,0.3452964277,
168.1589696,70.15182476,38.18530375,23.317205,15.15649693,9.996484164,8.296586685,4.94006452,3.658380479,2.643753742,1.357050445,1.142929391,0.7941333408,0.5603497854,0.3833948043,
185.213171,77.62217,42.48055181,26.12563018,17.15956078,11.75390476,6.625333145,4.142708664,3.057616317,2.342970145,1.687629438,1.110944222,0.8232491937,0.5862447347,0.4059163818,
247.8110771,102.7501669,56.33896878,35.07749316,23.48009026,16.4433171,11.85557819,7.476717659,4.46101965,3.338279163,2.535530373,1.908946175,1.20855084,0.9612885763,0.7446164113,0.4957496525,0.4723366554,0.3509358959,0.2791666814,0.1944734172,
291.9751808,127.0495108,71.59377755,43.80534806,28.13400454,18.8252282,13.01911321,8.700260746,7.03381941,4.671645422,3.443413335,2.32091911,2.029011631,1.311456774,0.9888820076,0.6800798086,0.5446067489,0.4164338999,0.2963635116,0.2133533196,
281.3411726,113.8365221,100.0441554,62.70250655,38.42709652,25.38189185,17.54862444,12.4921108,8.995568003,5.946958924,4.760698689,3.586304133,2.059606403,1.634478112,1.211484199,0.9050898419,0.6211982276,0.4551821569,0.3321585796,0.2366379682,
302.971863,128.0326446,92.04611441,66.27300206,41.14983869,27.10669479,18.63037042,13.12198091,9.699625173,7.43991784,5.129030308,3.83101315,2.252283262,1.615042681,1.250479038,0.9414537694,0.6889561568,0.4838202145,0.3489372537,0.2476728407,
345.3924955,150.3763296,85.12779911,52.36966882,33.76588567,22.69864571,15.84545842,11.93130386,9.332586263,5.495105458,4.09079317,2.383089868,2.118391354,1.540252416,1.158332743,0.8045641149,0.633159318,0.4901483745,0.3497243257,0.2495519625,
352.2930638,149.3501129,97.2585093,74.05521442,47.60026482,31.64833038,21.83301076,15.49963731,10.10031702,8.486443193,5.795459213,4.337308224,2.47897933,1.902728578,1.428412422,1.080910782,0.7858401205,0.517381658,0.3522313274,0.2409137522,
415.7075594,174.9997512,99.65366876,63.98265807,42.57879082,29.30342008,21.06708764,15.76628104,9.783786046,6.231414365,4.706201112,3.742479474,2.68023543,1.994691068,1.486623759,1.07466465,0.6765895728,0.4699497324,0.3503591186,0.2576957702,
416.6009511,173.1405055,95.35685969,59.29094938,39.06671147,26.69863753,18.98895797,14.85006968,10.54378477,6.386503129,4.784079987,3.065187422,2.56616861,1.98501505,1.469126943,1.052295903,0.6820678962,0.4931829873,0.3693614246,0.2675393597,
401.0663393,159.863123,130.1217224,92.57308337,56.03528121,36.8401046,25.30495746,17.8675367,12.11934469,8.998327897,6.798281064,5.074952674,2.936751806,2.22745795,1.700286247,1.291694913,0.9255814362,0.6001719279,0.4140458296,0.2877176533,
456.8580778,189.8540503,106.7725526,68.53797706,45.68861591,31.24185295,22.22947315,16.79286518,11.66634449,6.999530846,5.290389553,3.060699749,2.453021677,1.822107218,1.356093508,0.9627977425,0.7202714426,0.552907807,0.3968277977,0.2805027094,
486.7535683,199.4523924,107.9587537,65.7542003,42.60452912,28.75708727,19.99829209,13.85716504,10.44231276,7.447577903,5.565822926,3.229253786,2.356405726,1.779479939,1.35195754,1.090908639,0.7928990421,0.5404811708,0.3775491981,0.264380907,
512.9679987,207.8740936,113.0871427,71.75131396,49.08407727,34.29370248,24.40435484,17.7738767,13.28535378,7.571342689,5.766292469,3.313864831,2.702981884,1.967426546,1.44646497,1.0527855,0.8626287736,0.6086692723,0.4240565151,0.2959536822,
558.2494496,226.4296743,121.7185034,73.86633291,47.91685792,32.47429139,22.73698966,15.79082381,13.38963392,7.940715019,6.030113075,3.464024818,2.875515486,2.085503359,1.460277108,1.349090556,1.156832197,0.6891300342,0.4463413806,0.3853749784,0.3389240785,0.2079433769,
609.2832789,252.1655442,169.4440883,116.8749089,73.32235134,48.62391608,34.17715371,26.36409171,21.08448934,12.26318138,8.342469494,6.305740762,3.605294739,2.996867394,2.194507252,1.651710146,1.198057788,0.8029006377,0.6620027251,0.5024931671,0.351932924,0.2414049668,
644.6274485,261.8229951,144.078437,92.43692367,62.86753222,43.16472965,30.20912639,21.70859531,14.11156707,8.380328117,6.390721339,4.082381195,3.555081727,2.577939754,1.946817703,1.380202815,1.116339834,0.9120615072,0.6304779489,0.5112415711,0.4026277089,0.2803203328,
706.8192098,286.5829404,193.7305004,134.3997364,81.01464632,51.67935435,34.69528586,24.27610075,19.11619555,13.10290441,8.963653652,6.797643007,3.877506022,3.563582608,2.552969247,2.035144669,1.639421353,0.9110597165,0.7061245011,0.5658285306,0.4393732525,0.3127700369,
779.8412013,318.2937439,190.5917647,128.0513861,80.29279386,51.74401485,34.90745091,24.58616137,21.54359266,13.86653922,9.13638984,6.975806444,4.23486896,3.606935864,2.743091982,2.191396637,1.810853322,1.002590265,0.8787789432,0.6429495392,0.4676723201,0.3337690369,
767.4340133,316.7796273,196.3363099,140.4403827,88.95480401,58.34796849,40.37670332,29.27952257,22.03029242,15.98383985,9.318021963,7.162322725,4.441772972,4.074671608,2.837335935,2.169259487,1.598625443,1.130078846,0.9599506097,0.6883019468,0.4969543239,0.3538874016,
819.4557174,333.6557034,199.2942814,138.1573988,87.53643509,56.48512197,37.97024306,26.40355329,18.139476,14.27982077,9.907137312,7.531041111,5.449912761,4.737984847,2.991997713,2.298821839,1.468053569,1.196622977,1.039422508,0.7631919555,0.5543694752,0.4394845731,0.3289476706,0.298587488,0.1945346165,
890.9256744,385.1139971,263.8276185,169.2487687,107.4595188,73.93932258,52.34154008,37.09975142,26.68581207,20.03708059,15.48146539,10.17531075,7.803992957,4.689966547,3.599155404,2.835883525,2.278253022,1.490421854,1.262318308,0.9488474809,0.7357840057,0.4177128368,0.3822834027,0.2935364151,0.2135039086,
964.1591584,392.2592001,261.6200438,195.6309968,125.299017,83.31687434,56.11365488,38.57392551,27.17092154,17.48417063,12.69026436,10.82716054,8.076958356,4.917529635,3.661164697,3.027467856,2.453870513,1.676098288,1.184091643,0.978010819,0.7696837903,0.5012476224,0.4255418264,0.3097935684,0.2204437116,
988.323808,410.912174,288.9090104,200.8592877,134.9204979,92.12357632,61.59331018,41.95585872,29.40470688,21.11119362,16.17412171,10.91571129,8.343933056,5.062319428,3.575058718,2.859216103,2.46049292,1.647766698,1.283714453,0.9691347063,0.6522259716,0.608679874,0.4565306802,0.3291512601,0.2370772659,
1005.640939,392.7578799,311.7099994,209.7852471,129.7977497,91.06455553,65.03071126,45.9259624,32.90647618,23.49400993,19.38205405,10.89618149,8.466436475,5.29660039,3.634504665,2.941750673,2.502838679,1.805723321,1.307400193,1.032091283,0.8005040774,0.6213049396,0.4616912551,0.3305797468,0.2313691315,
1077.467054,432.0851179,324.9088093,210.141308,127.4777766,84.53322873,58.8619724,41.50544601,29.50616869,22.05028472,14.74808986,11.99258505,8.9380458,5.361781803,3.907521588,3.284032536,2.852602846,1.86794102,1.40984881,1.089270452,0.7893767478,0.5259471,0.3837566638,0.3252548785,0.2398767288,
1183.028435,479.2438856,265.8036052,177.3239723,133.1337592,94.59911207,64.15050722,43.95724272,30.84147017,22.17278434,16.77602714,11.66931625,8.805687329,6.912382948,4.929193869,4.261393555,3.147378167,1.936787397,1.377914199,1.04966703,0.7909694002,0.639692466,0.4836918627,0.3467886345,0.243877338,
1257.295026,504.4894172,279.8665992,201.99602,142.5910659,94.95570477,64.42775862,44.68365544,31.66461622,25.31702844,16.80013594,12.36571748,9.413845513,5.673718547,4.77539772,3.713643644,3.018320567,2.14548049,1.462672386,1.210183909,0.905666353,0.6354225327,0.4892273071,0.3704872292,0.2589115216,
1297.396045,522.8360909,304.2728434,219.3518365,149.1315201,98.82874825,66.36413963,45.5056286,31.87495951,23.48905532,14.76424344,13.37770203,9.710295632,5.949356006,4.113983771,3.764158641,3.21819303,2.202148752,1.485086234,1.198308606,0.9139712917,0.65706123,0.4783112689,0.3521750985,0.2513792871,
1414.951829,561.1158065,305.5964281,205.9336888,145.9262524,99.64440895,69.59248631,49.84846361,36.54992703,27.8418891,20.49926969,12.60737958,9.803208119,6.14094254,4.442723709,3.876313606,3.278232605,2.264682832,1.667519703,1.321304051,0.9627478429,0.6625764711,0.5184419736,0.4476582044,0.2921212916,
1357.402521,547.4267562,339.4465326,247.3230561,156.8785438,102.9611932,69.83653966,48.45017614,34.33199251,22.67259531,19.41621512,13.29643856,10.20580236,6.211669087,4.561695097,3.66305144,2.894962801,2.333449461,1.644293748,1.271978464,0.9222156825,0.6561166055,0.5395777219,0.3984731384,0.2707642388,
1475.867729,594.6909412,356.6801704,247.650086,157.1817057,102.3629729,69.6424209,48.98880264,35.32895216,26.82180675,20.00319171,13.53270638,10.45563462,6.354806552,4.829742206,3.858981737,3.223435465,2.422950345,1.737096781,1.361783285,1.010367933,0.7257370826,0.5300778499,0.3904497522,0.2808952029,
1687.612633,678.4772699,381.938132,256.0905783,186.7605802,151.8816771,101.925852,68.39168025,47.2170396,33.15280906,27.00957226,17.62135034,14.07965551,10.72228921,6.555284333,4.993799823,4.02786567,3.252948481,2.557952512,1.898196074,1.510515274,1.138458073,0.8227321569,0.6251497293,0.4782096496,0.3728363341,0.2975276054,0.2025224555,
1812.280547,851.7240648,594.708512,336.7069148,202.6520035,134.4714458,95.72626174,68.8061341,49.22720331,35.60781455,26.10406446,20.93140254,14.04243474,10.9098979,6.792753857,4.88179059,4.015899428,3.098649703,2.675897433,1.759257977,1.412870531,1.155119829,1.031686522,0.7384771872,0.5271324739,0.4028424791,0.3182368143,0.2282784966,
1921.498044,809.3123704,591.1976525,365.6787273,226.680963,150.6752334,102.3217017,70.25439611,49.21623299,35.50934448,20.9131217,18.25821468,13.20927106,10.39968015,7.280105277,5.494012123,4.497886467,3.48063976,2.866064022,1.765835405,1.46971339,1.204845879,0.7649433874,0.6578731671,0.618905164,0.4300060953,0.3256163494,0.24606401,
1856.909951,726.3335076,513.3520047,371.5631988,256.5705561,203.2778452,135.4014113,91.34801701,62.91938939,44.16304475,30.22520691,25.91022192,17.36416482,13.92219764,11.11775205,7.231609226,5.159967994,4.277379663,2.676734197,2.285786778,1.700007276,1.308043317,1.227563688,0.8083473876,0.6301096389,0.4958901189,0.3736739715,0.2708283571,
2205.808871,929.170523,538.2834377,344.688146,247.7913215,172.4034585,113.6344197,75.87735334,51.96677806,35.43271472,32.96011931,22.81463829,14.52084775,11.12031004,8.696361006,7.100882694,4.930233336,3.991650517,2.991211873,2.123012146,1.783145028,1.335663823,1.13310041,0.8294830643,0.6065670622,0.4573971119,0.3934075838,0.2999460318,
2058.928763,816.6760493,654.2851384,417.935327,258.2198286,172.1174181,116.5191648,80.15158768,56.57910348,40.9037462,29.67643487,23.74815642,15.69228304,12.18673707,7.16139534,6.212980573,4.611111467,3.266115372,2.950505834,2.113869462,1.71755178,1.420030308,0.9152398008,0.8157734918,0.642832976,0.5642593313,0.438715018,0.3203855755,
2373.335796,1002.419768,766.5523858,492.6656938,312.3351393,214.8895087,147.4734005,100.3663349,69.24607054,48.81327844,34.81332616,27.01400414,20.07931182,15.28709903,12.0590288,7.781882302,5.556656138,4.816153922,4.074713245,3.170888331,2.013855587,1.541068966,1.360162876,0.8929628346,0.8044158732,0.6815804575,0.4908763103,0.4188913917,0.3642850587,0.3366929907,0.2388388013,0.193142727,
2591.554104,1081.276785,705.9956194,473.915368,389.3293945,274.5418905,195.4052921,135.5158539,91.95032244,63.5041565,44.95658403,32.60954419,23.78640485,18.06699644,13.72712553,10.84814837,8.107716848,5.975393532,4.930500601,3.567107808,3.299984433,2.199364253,1.811438664,1.345349901,1.105640752,0.8510489146,0.6452889291,0.5852073325,0.4225870159,0.3011100463,0.251288014,0.2012874959,
2767.014874,1152.41953,729.8381075,516.9643022,429.6995313,282.3686522,186.0900401,129.8952693,95.83017743,72.83362264,54.6703198,40.78508611,22.54377767,18.4584874,13.83975752,10.06541961,8.715969647,5.714512048,5.200857504,3.951950238,3.421349538,2.239269817,1.90115319,1.237908193,0.9491854766,0.7960982672,0.6954189701,0.5464908673,0.4114060196,0.3080301674,0.2870399345,0.2151699445,
2838.226518,1161.681537,717.9885389,472.6479743,299.166136,211.0071548,160.8782962,112.5377399,77.84646528,54.72646461,38.82901188,30.63783582,21.63488263,16.39299488,12.72833347,8.834971598,8.063266506,5.47464839,4.457662334,3.398329659,2.513953921,2.028874638,1.476446754,1.119496673,0.9844627941,0.7390188238,0.6061648984,0.432054588,0.4094877593,0.2882502541,0.2243091394,0.1860246059,
2772.830361,1216.923328,883.2199791,520.1009083,323.6716231,233.6593252,168.3414931,115.0570223,79.38409254,56.08944453,40.64300718,30.9715633,25.18848205,17.09868453,13.42248394,8.124944426,7.151207813,5.286776182,3.8630809,3.287001193,2.643129795,2.043838053,1.517557785,1.082207932,0.9383978602,0.6857506967,0.6230723802,0.5185762133,0.4657974667,0.315380077,0.2651351599,0.2052848143,
2966.443613,1159.813901,740.4025993,599.1914903,408.1537636,284.7745619,190.994641,137.6908751,107.251675,77.79633824,55.11345949,38.06966336,33.32678962,20.49233431,17.71334775,13.64207911,8.627520296,6.247161351,5.264047974,4.060444501,3.541953062,2.446988886,2.005826717,1.277362699,1.164711903,0.9038354032,0.6826142022,0.5656676807,0.4548393332,0.3402490823,0.2889096606,0.2117314289,
3021.288507,1254.401349,836.413533,541.9098112,344.7689059,252.0904284,184.5860683,127.748368,87.98794607,61.54774849,44.12915446,32.55331397,25.92914755,17.95236066,14.03281054,8.483716526,7.472829884,5.549207661,4.528662014,3.554561625,2.599154533,2.087901189,1.341134301,1.098615522,0.9281569334,0.7770881906,0.6208020401,0.5160571228,0.4519186055,0.3414888549,0.2892386195,0.2121892198,
3293.073914,1328.941553,838.0111818,557.6518514,353.196088,259.6105462,188.188893,127.930917,88.16683575,62.13863362,44.74588151,32.15216197,26.17896541,17.9473584,14.01311675,9.060850294,7.95133815,5.84453468,4.373927387,3.810931974,2.731569404,2.218292061,1.606370655,1.297030761,1.052354461,0.8150415364,0.6627958094,0.5266627517,0.4784668703,0.3076894506,0.2755970918,0.2175677665,
3250.25572,1267.314696,894.2479456,582.8069255,341.4187127,257.6653017,205.3540845,134.3740283,90.51889289,62.7566359,44.33121943,36.81637429,26.63630986,18.59653997,14.54948532,8.924867048,7.717243324,5.786785172,4.657897255,3.431747273,3.265945001,2.293983396,1.559327755,1.307788097,1.112472375,0.8164628883,0.6686876259,0.5037947796,0.4421333962,0.384129581,0.2837603514,0.2105251529,
3448.239801,1369.664297,905.2876667,611.1107612,385.1927322,272.7583007,195.8740482,135.1353449,93.75222289,66.18690125,47.62715909,31.4163515,26.30790481,19.28236042,14.91954534,9.242074409,7.380314,5.932671048,4.616794865,3.97157321,2.619443485,2.108534544,1.579104435,1.343630311,1.012177147,0.8878645741,0.6666123266,0.5634558528,0.5166174794,0.3552870431,0.3086039144,0.2227599785,
3594.003392,1402.405551,770.6309101,533.6543936,373.3096703,270.3356366,192.2407172,131.7670789,90.96428126,64.11274562,46.20801913,34.39269608,24.73549453,19.87666937,15.28507279,9.316772865,7.442959462,5.861101367,4.637106277,3.482219581,3.235191621,2.348939707,1.647716351,1.310430746,1.13103611,0.8491496594,0.66534793,0.5533634213,0.4960031633,0.3744890359,0.2908878719,0.2152226916,
3817.145798,1478.912817,820.1649534,595.5020413,402.1783239,284.3170387,206.3072663,140.9922283,96.08082858,66.80028923,47.60273571,34.04198552,25.48474947,19.57602479,15.2944703,9.695894037,7.491697989,6.081518659,4.498942492,3.599013839,3.30000254,2.399321829,1.568528345,1.443883007,1.1637411,0.8737146971,0.6825360584,0.5322968486,0.4744627235,0.3449200922,0.3206386689,0.2256218141,
3879.22924,1514.016848,863.9953527,612.0448456,391.1106423,255.3876575,186.1506554,141.8653229,101.6595485,72.01874749,51.54380357,39.411393,26.54036651,21.31846816,16.06214763,9.499629055,8.057774515,6.167791626,4.545781541,3.500118272,3.322572823,2.41831347,1.756279845,1.387467207,1.134643549,0.8886300344,0.6902565588,0.5384649719,0.4936940571,0.3792936369,0.3104265082,0.2237960634,
4224.283211,1603.649313,940.384356,765.7594652,455.1863608,290.7187395,202.6537858,144.3616829,101.0511412,71.04937815,50.79400192,37.7855997,28.42003544,20.47323115,15.89049427,10.85245549,10.34371551,6.811984754,5.650280526,4.280809655,3.490584289,2.681107658,2.065000353,1.473343452,1.270124162,0.9495005377,0.6969567878,0.5606206739,0.5223409174,0.441811874,0.3078061046,0.2212275367,
4202.91746,1623.872973,1147.944079,734.0880122,436.8188541,309.7940537,227.972062,152.8280199,102.7981322,70.74044134,49.69402484,37.81329643,28.98532542,19.96419116,15.33169098,11.52594995,9.566275191,6.939134169,5.350040844,4.542809474,3.100289551,2.710492434,2.155323514,1.380607865,1.116187181,0.930305825,0.73933848,0.5290909298,0.5023008511,0.3963188981,0.3170579395,0.2273705896,
4559.996725,1740.843479,935.0950182,727.7002761,471.4584948,295.1654322,193.487718,132.9766507,103.632537,86.08952882,63.72213455,48.17169138,32.27518913,22.60311101,17.9150668,14.3021814,10.91164074,7.088258503,6.083128662,4.483180678,2.957019517,2.344054035,2.020175113,1.478468624,1.134314645,1.059727761,0.8045265048,0.5591283359,0.441861519,0.3077095887,0.2605072686,0.2419189988,
4838.859739,1848.4788,987.479822,674.6398971,455.7803364,294.3357379,195.7376739,136.520519,104.417047,81.55522684,60.02825598,41.84406393,36.8266176,21.8751051,17.37529538,12.42803331,11.58611683,7.062779018,5.603733801,4.596899041,3.129224828,2.568435296,1.896845365,1.554606408,1.311456457,1.024585314,0.8256241233,0.5043141917,0.4599967674,0.4342833603,0.2934920289,0.193483206,
5277.568337,2019.6465,1060.079179,654.5769122,434.4058949,304.0956136,220.6638865,156.4628535,109.7297797,77.52953266,54.97367219,51.26818201,27.8421774,24.03704293,18.37736184,15.97047388,11.04924911,7.559988635,6.615015551,4.58687463,3.28249231,2.667814758,2.047257533,1.798125673,1.295469371,0.995432509,0.8184164863,0.6055874776,0.5110208802,0.4197647663,0.3115576078,0.2185833502,
5260.185218,2043.006461,1088.756828,675.9464086,476.6684128,357.1808225,249.5388734,171.5025933,119.1209,84.73784407,63.51913945,51.69544718,33.92051517,22.31339061,17.43229605,10.90597947,9.843420756,7.226400244,5.746229286,4.561666005,3.713070027,2.82321088,1.955865543,1.584675752,1.456527115,1.040069832,0.8850972596,0.70264196,0.4885891024,0.4153252376,0.346558982,0.2510063744,
5696.167995,2203.049776,1242.192891,862.1859378,568.2019044,372.8773365,247.6518448,165.95396,112.7243044,77.96233634,54.40109139,45.58788996,29.81661156,22.74181101,17.57306138,11.63479067,9.10685676,8.340190157,6.982618174,4.755017385,3.561976443,2.883467956,2.209419687,1.366609367,1.283596613,1.095748182,0.7939039992,0.6299935896,0.5904023941,0.4510403175,0.3604885796,0.2670689892,
6129.341491,2272.992707,1151.098092,761.3800356,590.9332386,386.498373,256.4853641,174.6204189,121.6034647,87.43161972,66.94831712,53.7335141,37.01070109,22.59707934,17.45899145,13.13936197,10.72452813,8.204554964,6.843189273,4.989069679,3.704727178,3.149122409,2.515669622,1.369286229,1.27380647,1.208823495,0.7252222266,0.6595237911,0.5936925248,0.4890784221,0.394715609,0.2801090823,
6411.03446,2552.39389,1463.414974,980.3575039,680.2076381,451.5537776,292.1266106,191.5460785,129.648153,121.7573601,88.44830213,62.54987693,45.2043448,34.57862942,24.23743066,18.70796783,11.02402431,10.42518929,7.549803021,5.425865191,5.149125121,3.403110718,2.805004689,2.041986221,1.4397174,1.15351417,1.004307221,0.8338788971,0.7031145575,0.5195458642,0.3892076618,0.2848662634,
6324.821449,2411.273668,1468.735353,1105.196843,693.6781409,461.9708776,314.146683,215.7351713,153.3578185,112.1917631,81.63923619,58.83219464,48.0837831,32.57727267,24.19291878,18.69082695,11.98772387,8.552122963,7.520562617,4.838960798,4.524139008,4.115929287,3.159797772,2.532294492,1.470997479,1.115451903,0.9789504574,0.8726323195,0.613196259,0.4763166772,0.4163457746,0.3015903845,
7135.270424,2778.834309,1501.057321,990.1321859,809.6729049,542.6253453,351.5388602,235.5947214,164.1990148,116.9637314,83.97908683,60.77027993,45.75207291,31.33778125,25.72274784,19.42976069,11.5977491,10.24123038,7.75674593,5.51043749,5.142516743,3.654735943,3.00609236,2.388464961,1.492381341,1.184744541,1.0418661,0.9002896823,0.6436245746,0.4919690336,0.4425356923,0.3049494237,
7481.072956,2831.332146,1680.196866,1198.303002,730.06323,466.5482259,326.5539002,241.9763217,173.4248981,122.0012197,86.44102429,62.01643856,48.63427018,31.93195967,26.13054418,19.77676718,11.521835,10.78962859,7.83476668,6.153443823,4.918095598,4.173373715,3.22850225,2.774966663,1.617192936,1.540823039,1.130930245,0.8303133848,0.7337911338,0.5866473242,0.423663521,0.298032916,
7679.362823,2903.964836,1579.153353,1139.145081,775.2342827,514.8104148,346.2889126,234.9833493,164.8516573,119.7170704,87.38003855,63.19782845,53.22766856,31.03200622,27.05793038,20.07777426,12.29119206,9.59927551,8.072424113,7.513604539,5.404790441,3.652805904,3.015538466,2.310558242,1.686514473,1.435961496,1.163084987,0.9167898341,0.6624297261,0.5623029726,0.4663388886,0.3247248235,
8435.422869,3122.329246,1731.145876,1603.687077,897.0760794,601.1946124,464.4421063,355.3649678,301.2420116,199.5089517,135.9995881,119.0096109,90.5400981,64.2453539,39.17063577,25.36481109,19.81968663,14.17274263,13.00649625,8.673415303,7.548592817,5.457934885,4.401838925,3.779994531,3.196808829,2.284944037,1.567397035,1.221551764,0.966146314,0.7072105274,0.5633935259,0.5177355995,0.3413653366,0.2477704119,0.186620859,
8973.983704,3433.325358,1976.79395,1318.278173,865.2169303,655.5713258,463.4533962,330.4475625,238.6318186,166.8305901,116.1671201,82.24270942,60.05581947,40.80690024,32.13676943,24.86447169,19.82538711,12.92262482,11.63626566,8.547918272,6.16761599,5.850356752,3.864620664,3.297934375,2.172749028,1.63554117,1.257071113,1.096679448,0.8637627388,0.7524673847,0.5883564396,0.4961964309,0.4103807403,0.3095735018,0.2183634356,
9645.757361,3685.755636,2129.400297,1628.649551,1141.878918,767.5354821,502.6857747,380.6073098,319.1385239,219.4214262,153.5258882,109.9642219,79.88792727,57.86200807,46.1863618,28.80598186,24.62164045,19.96321323,13.10356131,11.7470889,8.613374027,5.931813812,5.63370482,4.392113212,3.487920875,2.229107511,1.651274217,1.327620083,1.218459151,1.00431013,0.8519183611,0.566034067,0.4375574728,0.3786411771,0.2579538273,
10258.95153,3842.671138,2032.272654,1637.304681,1298.745853,849.0684272,563.043461,393.7510027,301.9179721,229.872186,166.8571777,119.3540824,85.64623602,62.39731738,44.04513256,36.41264687,26.4507185,20.84593151,13.15643572,11.33511072,8.684246473,5.530221063,5.133713954,3.951185721,3.446278864,2.303316228,1.798374207,1.399968553,1.107528705,0.9051252681,0.7379017103,0.5589328314,0.444009867,0.3976445863,0.2772291615,
9573.891424,3362.666856,2527.509438,1935.376256,1339.996907,910.0213014,570.3933293,392.3850985,356.1256932,246.8729623,169.7753835,118.6063108,84.21540559,60.54404597,45.88485989,38.56056797,27.00490911,21.26071115,13.33289528,11.30435753,8.777516715,5.831812435,5.392893715,4.056884616,3.27126851,2.748927389,2.043148603,1.626763063,1.205669279,1.011329103,0.7840297749,0.5627742611,0.4816186271,0.3967561606,0.282470009,
11404.10702,4205.958106,2234.26648,1917.320831,1245.651455,942.7059508,767.1327722,565.3008393,386.6547456,265.399128,192.46735,149.8868969,112.7679612,82.4016017,59.51597161,49.25391547,29.65073427,26.88562537,21.47608742,13.87431576,9.582961107,8.202730866,6.217133332,5.494418963,4.061368319,3.200899166,2.837150053,1.787466836,1.496196316,1.24088498,0.8210796027,0.6044100388,0.5075958116,0.4325875877,0.308722304,
13564.94128,9632.241538,6789.077575,4711.503868,3253.026278,2206.934373,1573.491225,1119.307989,821.8965406,575.6426233,428.5470489,326.0551984,236.6509026,175.3489117,134.4987737,101.2724025,74.78001371,55.98300103,42.04263136,30.00526383,23.352055,18.54131588,14.38831352,10.42569468,9.050572189,6.961879234,6.01757589,4.434808377,3.728826931,2.869622689,2.468248141,1.879914556,1.407023724,1.23249905,1.070162843,0.8736239408,0.8325735583,0.657178179,0.5285800025,0.4456771275,0.402733459,0.3527229267,0.2891063956,0.2406523488,0.2000374465,
16736.11753,10801.30728,7617.313228,4937.336193,3673.522307,2507.457445,1789.938785,1281.370755,933.4592835,652.4528127,475.0475574,357.105244,255.9935269,183.3162906,136.6487697,105.5183613,79.29226903,57.31440877,44.02213011,33.69712081,25.29190464,19.89535864,14.69214699,12.0116421,9.3007297,7.219344549,5.909990512,4.780339776,3.781230214,3.141120633,2.407391264,1.97503633,1.562350799,1.339536879,1.039412279,0.9220055895,0.7615898279,0.6134844138,0.5412295428,0.46793873,0.3872457579,0.3418671467,0.3034422663,0.2617352441,0.2240929896,
17355.6452,11565.44911,9070.897913,5715.820274,4028.368448,2981.507135,2205.94124,1582.151629,1069.008874,761.4123409,576.5465822,417.8911445,303.3641974,225.8587459,169.3989698,128.0918756,100.2783398,77.52539688,57.62554044,42.49043917,33.44045545,25.02246367,18.79102411,15.39136132,12.11428631,9.531868034,6.820858766,6.252921478,4.778236546,3.951013983,2.724274935,2.316877281,1.939660015,1.620886415,1.253794838,1.082250195,0.8595812539,0.7334534607,0.5913327481,0.50344441,0.451434745,0.3724249186,0.2886812238,0.2670631854,0.2074602878,
18706.22046,13450.96747,9233.480023,5908.154189,4326.573572,3131.582325,2194.809585,1703.342571,1137.744425,793.9079951,615.929652,442.2841059,319.2838926,237.8852773,177.9725353,133.856203,102.442206,78.19660571,58.85771664,43.36848553,33.52228609,25.35033375,19.47676336,15.35272824,11.61352053,9.630159903,7.196002931,6.324085705,4.810568385,4.025110898,2.788845118,2.410502999,1.99820148,1.657137409,1.299736693,1.148869612,0.872881968,0.7486860537,0.6201664712,0.5152893313,0.4730358612,0.3823653554,0.2954457141,0.2716560031,0.2243950735,
19861.07126,13077.16124,9216.901796,5753.208945,4231.331322,2822.373758,2017.458219,1426.852653,1055.289799,734.1716589,526.1848319,390.9694464,277.7748518,196.0828225,144.8429876,112.0896679,84.36257148,61.74413601,45.87004936,35.87786284,26.95835077,21.57804857,15.14751998,12.42303459,9.708419075,7.511754778,6.213045789,5.055119675,4.046768711,3.153539032,2.521528633,2.106531666,1.66539063,1.44931464,1.121301582,0.9890759597,0.8335557318,0.6613362276,0.5476711185,0.4594310286,0.3996323623,0.3587051812,0.3229697958,0.2828252977,0.2347234905,
21572.27597,13592.29085,9706.56852,6397.606719,4225.328215,3072.79401,2189.238557,1442.583374,999.2563713,753.8613501,546.9738977,395.3746492,295.4715244,216.3723669,156.9547058,115.2748109,85.67684058,63.26054773,49.87496545,35.00917389,27.63001706,22.27087385,15.45291302,12.31527534,9.960613692,7.370222855,6.695655364,4.697597004,4.050598189,3.198430737,2.703175493,2.152621149,1.741971374,1.344345224,1.141264953,1.038402578,0.8061446402,0.7001916138,0.5597850212,0.4775072827,0.3927304648,0.3710291431,0.3323203846,0.2578005101,0.2431743778,
18699.87177,13452.03168,9559.803389,7537.951329,5289.245817,3789.478945,2649.324068,2310.190214,1581.714041,1208.684676,920.0451107,681.6013666,505.7514868,373.8611245,283.1999585,226.859854,170.8820781,125.9847076,97.51973443,77.09214025,58.82024076,39.88013963,34.51094185,25.65862686,20.21358789,15.28726812,12.82292811,9.919730929,7.27957286,6.40970878,4.925410589,4.149691756,3.042482482,2.334725439,1.985000395,1.610711218,1.183393329,0.9609222383,0.7141951729,0.6780203618,0.5446373188,0.3969052242,0.3581683166,0.2923936473,0.2087187462,
21675.07521,12635.2418,9390.843549,6625.122057,5037.635653,3331.624626,2577.403024,1865.814926,1474.752813,1021.1666,760.2552852,593.8835033,429.1795088,307.9500509,225.4695008,175.529915,139.1000708,104.7904716,78.26210103,59.2557068,47.77938403,33.30107484,26.52350901,22.89117726,15.38155874,13.39862985,10.20439844,8.060529482,6.813034703,4.776402307,4.037797899,3.234918347,2.693508066,2.093793895,1.59588071,1.339075878,1.081252749,0.8563717727,0.698569849,0.5708151566,0.4919509854,0.4055679832,0.3166431225,0.2620009351,0.2028026504,
25471.05311,12753.77939,9469.790008,6960.674553,5181.846557,3323.637178,2715.361532,1950.350598,1480.895607,1012.392127,737.2545603,618.6815582,450.0402336,323.9739608,236.6685991,180.2280382,146.939761,112.2615286,82.72746724,62.34320192,46.32363013,34.92932574,28.05723012,23.7520541,15.72830339,13.50834555,10.43063493,8.711985861,6.908568082,4.929091481,4.245410408,3.234775742,2.56594976,2.176699206,1.701254437,1.337371458,1.157202604,0.8938949452,0.6964103395,0.567409124,0.5073530654,0.4446051282,0.3274464246,0.2534834077,0.198829183,
23996.27961,14422.90206,10454.12522,7361.975426,5492.963723,3960.32568,2904.752529,2093.244571,1629.372305,1075.576039,787.8562141,663.4343915,483.8430514,349.0603023,252.5740624,187.8994592,144.2471403,110.5475243,83.8631508,64.76874926,47.79639181,36.56104994,28.47330316,22.93093581,16.59918461,13.28074207,10.71336149,8.099320708,7.218738932,4.809095098,3.923255979,3.422746465,2.339875024,2.130843276,1.580677802,1.291434768,1.107437513,0.8362977137,0.7231201332,0.5669660475,0.4858865228,0.4271915215,0.3095919492,0.2554498111,0.1974726614,
25522.31114,16877.66094,11901.2782,7277.223353,5060.1342,3612.096683,2516.788661,1642.875375,1153.898914,872.6418355,625.1979602,432.9258033,312.1388494,241.2430878,179.5448209,128.8158021,92.73306892,67.75383695,52.1386266,36.12862595,28.32777501,23.23614397,16.51872592,13.05737914,10.63317813,8.444723343,7.044480245,5.085628119,4.254687956,3.459836686,2.703608842,2.335492058,1.875209709,1.385173638,1.273466225,1.060630725,0.8688758116,0.7337689957,0.5735161768,0.5041475915,0.4509624197,0.401856763,0.3237191561,0.2741897354,0.2546514932,
27894.91309,18447.80541,12390.65095,7692.874082,5058.832214,3833.897573,2644.122704,1678.797077,1171.074172,888.1706134,635.5439486,448.672584,331.403848,249.6878555,182.6134826,131.7584406,95.36339728,69.86675444,53.27964661,37.10417927,28.98988605,23.25096095,17.15358082,13.28676326,11.02433809,8.346498144,7.349239686,5.145253751,4.474105944,3.331436081,2.780889127,2.292176269,1.867726287,1.414991259,1.33696902,1.09530379,0.8839990617,0.7408894843,0.583438756,0.4881348154,0.4514597446,0.407037271,0.3339224416,0.2783868998,0.2460002967,
30204.49117,17478.0973,12939.625,7706.16372,5280.297369,3871.89865,2660.893625,1726.202281,1196.132317,910.5040902,664.5148175,467.4681873,332.887491,244.9750415,183.5981252,135.7485851,99.68751832,74.58752863,53.1723476,41.22274409,32.6873389,26.0977362,16.63488773,13.87203605,10.97461278,8.919866009,7.299769561,5.277735192,4.568942802,3.32697118,2.923894997,2.285634596,2.030487752,1.604462661,1.253413319,1.157605402,0.8315964688,0.7595603406,0.5965038432,0.5230050602,0.4643658407,0.4115458529,0.3457581655,0.2744045535,0.2501825953,
31428.99426,15539.39474,11743.79441,7089.595695,4881.47837,3280.645266,2442.226799,1600.311911,1072.626732,752.188557,534.8774002,382.3689985,276.3231981,200.9402713,145.6065829,105.4108062,76.8675742,58.11363647,40.24268969,31.65572469,25.16718515,17.86445722,14.89428214,11.57988449,9.386134863,7.596398176,5.103461979,4.44673557,3.339553593,2.83346586,2.306867168,1.853687254,1.542506279,1.434519049,1.05052933,0.9829553672,0.8224378603,0.6724480129,0.5717819427,0.5277355323,0.4604332015,0.3855320324,0.3418723051,0.2807465601,0.2555207604,
35172.06527,19745.79319,14313.52219,8849.629304,5897.374087,4181.712803,2772.520339,1777.766133,1257.553806,950.8937549,675.2783655,485.1205513,360.6930262,266.0975871,193.822859,141.3854652,103.5159044,76.86758264,55.43088962,39.51133259,30.53775557,23.87317668,18.35108235,15.06897357,11.5772643,8.553921515,7.837651292,5.318633059,4.732783758,3.543024699,2.833289389,2.504417843,1.903319973,1.450909656,1.260455284,1.071718539,0.9089586316,0.7767026458,0.5909607694,0.515111552,0.4573515562,0.4317330194,0.3569995686,0.2914190505,0.250063356,
39973.95188,19714.67974,14239.2962,8544.712612,6064.240747,4504.422641,2898.807242,1880.245192,1315.148932,1007.503336,726.8749099,509.8048376,364.6544343,266.7328913,196.908825,144.8417176,106.4655022,79.42372119,53.84644614,41.88263836,32.13036499,25.53065164,18.28024977,15.05095962,11.75375568,8.86575153,7.911052374,5.685886168,5.047771577,3.388547894,2.783774649,2.395458185,1.927418019,1.505277662,1.275997603,1.112291798,0.9188218549,0.7833454174,0.6056352054,0.5137063685,0.4704104899,0.4270613328,0.3671074979,0.2963404259,0.2439260851,
40993.99271,18460.14828,12092.33873,7492.592434,5560.519296,3467.940255,2390.589545,1818.091023,1245.986316,856.8199048,602.6253444,430.6013946,309.7699626,221.9565059,158.4054327,113.6350733,83.22930558,56.22070205,41.37086791,32.08997916,25.25366726,18.92256949,15.47619764,11.96587218,8.808639663,8.157377495,5.365266859,4.859335219,3.536291953,3.196095176,2.471005537,1.795782241,1.660186548,1.393567907,1.026409303,0.8666193784,0.6754665728,0.5902812177,0.5237493274,0.4852467135,0.4497341014,0.3034813339,0.2766060646,0.2533179761,0.1914744108,
44438.47362,19208.5208,13854.27495,7704.26434,5107.36024,3810.411977,2573.355452,1737.809115,1218.266509,885.7499599,623.3620043,429.6073822,300.4361739,215.089641,156.8201771,115.5257355,85.53553555,66.64861112,45.90804225,36.22596196,28.25681487,18.04517427,15.6024761,12.12833407,10.12384121,8.023317588,5.387098669,4.868712673,3.429971454,2.996858263,2.282894504,1.91066644,1.682641728,1.355904581,1.175202235,0.9057036612,0.8443630836,0.7015403752,0.5932310048,0.4833499881,0.4173633393,0.3707674972,0.3289759459,0.2750270478,0.2205745634};

	//starting index of each vector plus one more so that lengths can be calculated
	static constexpr int c_aIndex[105] = {0,5,12,22,32,44,56,68,81,94,107,122,137,152,167,182,197,212,227,247,267,287,307,327,347,367,387,407,427,447,467,489,511,533,555,577,599,624,649,674,699,724,749,774,799,824,849,874,899,927,955,983,1011,1039,1067,1099,1131,1163,1195,1227,1259,1291,1323,1355,1387,1419,1451,1483,1515,1547,1579,1611,1643,1675,1707,1739,1771,1803,1835,1867,1899,1934,1969,2004,2039,2074,2109,2154,2199,2244,2289,2334,2379,2424,2469,2514,2559,2604,2649,2694,2739,2784,2829,2874,2919};
};

}  // namespace psi

#endif
